Barty, who swept aside Yastremska in one hour and 25 minutes, is bidding to end Australia's long wait for a homegrown champion at the year's first Grand Slam. The last was Chris O’Neil, who claimed the women’s title at the 1978 tournament.
Barty broke the Ukrainian twice to win the first set but Yastremska put up stiffer resistance in the second to level it at 4-4. The Australian broke to go 6-5 up on four straight errors from the Ukrainian and served out to seal the title.
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Barty had suffered a surprise defeat to American qualifier Jennifer Brady in her opener at the Brisbane International earlier this month but the title win in Adelaide was the perfect way to end her preparations for Melbourne Park.
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She fired 15 winners against the wayward Yastremska, who committed 31 unforced errors.
"This is incredible," said Barty, who punched the air and hit balls into the crowd to celebrate her first title win on home soil.
"I felt like it was a great tussle and I had to play my best to get over the line. I love playing in Australia, I love playing at home.
I can't wait to get started in Melbourne on Monday.
Barty won her only previous meeting with Yastremska in Miami last year.
"Congratulations to Ashleigh, it was a pleasure to play the world number one and good luck in Melbourne," said Yastremska.
"I hope we get to play many times in the future."
Top seed Barty begins her Australian Open campaign against Ukraine's Lesia Tsurenko on Monday.
Barty, Stephens and Gauff knocked out of Charleston Open
WTA Charleston, SC
Barty battles past Rogers into Charleston quarters, Muguruza, Kvitova out